These two kinds of Pokemon mean I won't restart my Platinum and HeartGold games, which makes me sad because I always loved the stories and trying out new Pokemon.
I usually have a single "permanent" game - usually the most recent game, as that's the one with the most versatility in breeding, TM mining, BP accrual, and so on (e.g. Platinum). If I acquire a new game which has more utility than my current primary (e.g. SoulSilver), I complete the new game, then begin the long process of moving all the important critters and items from one game to the other. Eventually, my former primary is prime for restarting, and my new primary has everything I want to keep.
I'm a hoarder, so this process helps me weed out stuff I'm never actually going to use, like that double-flawless Zubat which I
may someday breed for a good Crobat when I
might someday start doing UU competition, or a Snorlax from my sixth run of FireRed, or so on. They're nice to have in the boxes, but when I'm looking at eight boxes full of critters to trade, six at a time, in painfully slow batches, the decision to release them becomes a little easier to make. (Especially when I made the move from LeafGreen to Pearl - with ten full boxes on LG, six at a time via Pal Park, and the difficulties in rolling the DS clock for another Pal Park session, I spent over a month getting it all done.)
I always keep every critter who was on my E4 team in the first playthrough of a game - sometimes on my second or third playthroughs, too, since I build different teams for different starters - as well as iconic critters, like the aforementioned Kanto Snorlaxes, Togepi eggs, gifted Eevees, and so on. In the end, even the ones I'll never use are still worth keeping, since I'll always need something to hold all the TMs and items I need to move to a new primary game.